UPSC CDS 2 2021 Math Paper

Let the LCM and HCF of two numbers be x and y respectively.
Now, according to the question,
‌x+y=536
‌x−y=296
Adding Eq. (i) and Eq. (ii), we get
2x=832⇒x=416
From Eq. (i),
416+y‌‌=536
⇒‌‌y‌‌=536−416=120
LCM‌‌=x=416
‌ and ‌HCF=y=120
We know, Product of LCM and HCF=
Product of two numbers.
Let the other number be P.

∴416×120=104×P[∵‌ one of the ‌
numbers is 104]
⇒P=‌

416×120

104

=480
Hence, the other number is 480 .